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This lecture covers the computation in vector space retrieval, including properties like ranking of documents, query keywords, and the standard for web search. It explains examples of document and query vectors, vocabulary, and query weights. The limitations of boolean retrieval and the key idea of vector space retrieval are discussed, emphasizing the use of free text queries to represent documents and queries in an m-dimensional keyword space. Additionally, it explores index terms, query weight vectors, and length normalization schemes for document vectors.